Let f(t) be the piecewise linear function with domain 0 t 8 shown in the graph b

Question

Let f(t) be the piecewise linear function with domain 0 t 8 shown in the graph below (which is determined by connecting the dots). Define a function A(x) with domain 0 x 8 by A(x)= f(t) dt. Notice that A(x) is the net area under the function f(t) for 0 t x. If you click on the graph below, a full-size picture of the graph will open in another window. Find the following values of the function A(x). A(0) = A(1) = A(2) = A(3) = A(4) = A(5) = A(6) = A(7) = A(8) = Use interval notation to indicate the interval or union of intervals where A(x) is increasing and decreasing. A(x) is increasing for X in the interval A(x) is decreasing for x in the interval Find where A(x) has its maximum and minimum values. A(x) has its maximum value when x = A(x) has its minimum value when x =

Explanation / Answer

THIS WILL BE HELPFUL FOR YOU AND AWARD KARMA POINTS IF IT IS PLEASE You can create functions that behave differently depending on the input (x) value. A function made up of 3 pieces Example: A function with three pieces: when x is less than 2, it gives x2, when x is exactly 2 it gives 6 when x is more than 2 and less than or equal to 6 it gives the line 10-x It looks like this: (a solid dot means "including", an open dot means "not including") And this is how you write it: The Domain is all Real Numbers up to and including 6: Dom(f) = (-8, 6] (using Interval Notation) Dom(f) = {x | x = 6} (using Set Builder Notation) And here are some example values: X Y -4 16 -2 4 0 0 1 1 2 6 3 7 Example: Here is another piecewise function: which looks like: The Absolute Value Function The Absolute Value Function is a famous Piecewise Function. It has two pieces: below zero: -x from 0 onwards: x f(x) = |x| The Floor Function The Floor Function is a very special piecewise function. It has an infinite number of pieces: The Floor Function

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